...quantities are proportional. If the products are not equal, the quantities are not proportional. 379. In mathematical investigations, when the relations...products, will not destroy the proportion. Thus, if a : b : : c:d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,...

...d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence, 379. In mathematical investigations, when the relations...of the means equal to the product of the extremes. 380. If four quantities are proportional, THE ORDER op THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS...

...quantities are proportional. If the products are not equal, the quantities arc not proportional. 379. In mathematical investigations, when the relations...quantities may be varied, in any way which will leave ad— be. Hence, 380. If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES,...

...fractions being equal, and the denominators the same, the numerators must also be equal ; and hence, the product of the means equal to the product of the extremes. (66.) The property of geometrical proportions which has just been proved, is the fundamental principle...

...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? ' What rule is founded on this equality ? Explain the common method of stating in the Single Rule...

...demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leasre the product of the means equal to the product of the...products, will not destroy the proportion. Thus, if a : 6 : : c : d, the order of these four quantities may be varied, in any way which will leave ad=bc....

...proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of ihe ratios; or which will leave the product of the means...products, will not destroy the proportion. Thus, if o: 6:: c: d, the order of these four quantities may be varied, in any way which will leave ad=bc. Hence,...

...proportional. 343. It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the ratios ; or which will leave the...of the means equal to the product of the extremes. These changes are numerous, but they may be reduced to a few general principles. CASE I. Changes in...

...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? What rule is founded on this equality ? Explain the common method of stating in the Single Rule of...

...:: D : C; B : D : : A : C, &c. &c. From each of which we may readily derive the equation AD= CB, or the product of the means equal to the product of the extremes. Many other properties might be presented, but we limit ourselves to this short discussion, and proceed...